Blank space underneath header photo on mobile

on default the fullwidth-slider is responsive. I am not aware that this behavior should not apply to mobile devices.
I guess you have entered a min-height option on styling tab:

You have already ensured that the font is hidden on very small screens. But you could just as easily make them smaller.

All you need is to get rid of the min-height option – the fullwidth slider is a responsive slider !

for the caption it might be neccessary to have for very small screens smaller font-sizes – or to set a part (f.e. the avia-caption-content to display:none )

you got a rule :

@media only screen and (max-width: 489px) {
  .avia-slideshow li img {
    width: 100%;
    background-size: cover;
    height: 200px;
    object-fit: cover;
    left: 30px !important;
    position: relative;
    overflow: visible;
  }
}

Remove the rules given to you by ismael first because …

remove the left position – and height – otherwise you will have a gray bar on the left ;)

then there are some min-height properties:

inline-styles

@media only screen and (max-width: 489px) {
  .home #full_slider_1, .home #full_slider_1 .avia-slideshow, 
  .home #full_slider_1 .avia-slideshow-inner, .home #full_slider_1 .avia-slide-wrap {
    min-height: 200px;
    height: 200px !important;
  }
}

and enfold css:

@media only screen and (max-width: 479px) {
  .home #full_slider_1, 
  .home #full_slider_1 .avia-slideshow, 
  .home #full_slider_1 .avia-slideshow-inner, 
  .home #full_slider_1 .avia-slide-wrap {
    min-height: 300px;
  }
}

don’t know where they come from. But if you like to see the full width of the image – these settings are suboptimal.

any height and min-height is not necessary here – remove everything that is noted in your CSS regarding this slider; or is set in the element itself!
This setting only exists because the background must fulfill the height of the content. See the comment next to the min-height setting:

Slider minimum height in pixel
This is helpful on smaller screens if you got a lot of text in your slider

However, this is not the case here, which is why you can drive responsively up to very small screens.

you got still in – i guess quick css:

@media only screen and (max-width: 479px) {
  .home #full_slider_1, 
  .home #full_slider_1 .avia-slideshow, 
  .home #full_slider_1 .avia-slideshow-inner, 
  .home #full_slider_1 .avia-slide-wrap {
    min-height: 300px;
  }
}

and an inline svg for that element:
is setting it to :

Element {
  padding: 0px;
  height: 300px;
  transition: none;
  transform: translateZ(0px);
}